1. Field of the Invention
This invention relates to an optical wavelength converting apparatus for converting a fundamental wave into its second harmonic. This invention particularly relates to an optical wavelength converting apparatus, wherein a crystal of a nonlinear optical material, with which the type II of phase matching between a fundamental wave and its second harmonic is effected, is utilized.
2. Description of the Prior Art
Various attempts have heretofore been made to convert the fundamental wave of a laser beam into its second harmonic, e.g. to shorten the wavelength of a laser beam, by using a nonlinear optical material. As an optical wavelength converting apparatus for carrying out such wavelength conversion, there has heretofore been known a bulk crystal type of optical wavelength converting apparatus as described in, for example, "Hikari Electronics No Kiso" (Fundamentals of Optoelectronics) by A. Yariv, translated by Kunio Tada and Takeshi Kamiya, Maruzen K. K., pp. 200-204.
As the crystal of the nonlinear optical material, a biaxial crystal, such as a KTP crystal, is often employed. How to effect the phase matching with a KTP biaxial crystal is described in detail by Yao, et al. in J. Appl. Phys., Vol. 55, p. 65, 1984. The method for effecting the phase matching with a biaxial crystal will be described hereinbelow.
With reference to FIG. 4, the direction, along which a fundamental wave travels, and the optic axis Z of the crystal make an angle .theta.. The projection of the direction, along which the fundamental wave travels, onto the plane, in which the optic axes X and Y lie, and the optic axis X make an angle .phi.. The refractive index of the crystal with respect to the fundamental wave, which impinges upon the crystal at an arbitrary angle of incidence, and the refractive index of the crystal with respect to the second harmonic of the fundamental wave are represented respectively by EQU n.sup..omega., n.sup.2.omega. ( 1)
The refractive indexes of the crystal with respect to the light components of the fundamental wave, which have been polarized respectively in the X, Y, and Z optic axis directions, and the refractive indexes of the crystal with respect to the light components of the second harmonic, which have been polarized respectively in the X, Y, and Z optic axis directions, are represented by EQU n.sup..omega..sub.x, n.sup..omega..sub.Y, n.sup..omega..sub.Z, n.sup.2.omega..sub.X, n.sup.2.omega..sub.Y, n.sup.2.omega..sub.X ( 2)
When k.sub.x, k.sub.y, and k.sub.z, are defined as follows:
k.sub.x =sin .theta..multidot.cos .phi. PA1 k.sub.y =sin .theta..multidot.sin .phi. PA1 k.sub.z =cos .theta.
the following formulas obtain: ##EQU1## Solutions of Formulas (3) and (4) represent the conditions under which the phase matching can be effected.
When B1, C1, B2, and C2 are defined as follows: ##EQU2## the solutions of Formulas (3) and (4) are represented by the formulas ##EQU3##
When the condition EQU n.sup..omega., 2=n.sup.2.omega., i (8)
is satisfied, the phase matching between the fundamental wave and its second harmonic is effected. Such phase matching is referred to as the type I of phase matching.
Also, when the condition EQU 1/2(n.sup..omega., 1+n.sup..omega., 2)=n.sup.2.omega., 1 (9)
is satisfied, the phase matching between the fundamental wave and its second harmonic is effected. Such phase matching is referred to as the type II of phase matching.
In cases where the type II of phase matching is effected with a biaxial crystal, the fundamental wave impinging upon the crystal is subjected to two refractive indexes of the crystal. By way of example, the nonlinear optical constant d24 of the crystal may be utilized. Specifically, as illustrated in FIG. 5, a fundamental wave 11, which has been polarized linearly in the direction indicated by the double headed arrow P, may be introduced into a crystal 10. The direction indicated by the double headed arrow P inclines at an angle of 45.degree. from the Y optic axis of the crystal 10 towards the Z axis of the crystal 10. (The fundamental wave 11 comprises the linearly polarized light component in the Y axis direction and the linearly polarized light component in the Z axis direction.) In this manner, a second harmonic 12, which has been polarized linearly in the Y axis direction, may be obtained from the crystal 10. In such cases, the linearly polarized light component of the fundamental wave 11 in the Z axis direction is subjected to a refractive index EQU n.sup..omega., 1 (10)
Also, the linearly polarized light component of the fundamental wave 11 in the Y' direction, which direction is normal to the direction of travel of the fundamental wave 11 and to the Z axis, is subjected to a refractive index EQU n.sup..omega., 2 (11)
Thus the fundamental wave 11 is subjected to the two refractive indexes.
Strictly speaking, in cases where the crystal 10 has been cut into the shape shown in FIG. 5, the fundamental wave 11 impinges upon the crystal 10 such that it has been polarized linearly in the Y' direction (which inclines from the Y axis towards the X axis) and in the Z axis direction. The second harmonic 12 is obtained as light which has been polarized in the Y' direction. However, practically, no problem occurs when consideration is made in the manner described above.
Japanese Unexamined Patent Publication No. 1(1989)-220879 indicates that, in cases where Nd:YAG is used as a solid laser medium in order to produce an unpolarized laser beam from the solid laser oscillation, and a nonlinear optical crystal, which effects the type II of phase matching, is located in the region inside of a resonator in order to yield a wavelength-converted laser beam, longitudinal mode competition occurs between polarization modes, so that much noise may occur in the wavelength-converted laser beam which is thus outputted. This publication also describes that noise in the output can be reduced by inserting a quarter-wave plate at an appropriate angle into the region inside of the resonator.
Also, U.S. Pat. Nos. 4,656,635 and 4,701,929 disclose that, in cases where Nd:YAG is used as a solid laser medium in order to produce an unpolarized laser beam from the solid laser oscillation, noise in the output can be reduced by eliminating spatial hole-burning in the solid laser medium. These publications indicate that noise in the output can be reduced by, for example, utilizing a ring laser resonator or locating the solid laser medium between a pair of quarter-wave plates.
Additionally, Japanese Unexamined Patent Publication No. 3(1991)-49278 discloses a technique wherein, in cases where Nd:YAG is used as a solid laser medium and an unpolarized laser beam is produced from the solid laser oscillation in the longitudinal multimode, noise in the output can be reduced by keeping the temperature of a resonator, in which the solid laser medium is located between a pair of quarter-wave plates, at a specific value.
Further, in Optics Letters, 13, p. 805, (1988), relationship between directions of polarization in two longitudinal modes and mode stability, which relationship is obtained when a laser beam is produced by a solid laser medium from the solid laser oscillation in two longitudinal modes and is caused to impinge as a fundamental wave upon a nonlinear optical crystal which effects wavelength conversion. Specifically, in this literature, it is reported that, as illustrated in FIG. 6, in cases where the direction of polarization in a first longitudinal mode and the direction of polarization in a second longitudinal mode incline 45.degree. with respect to an optic axis of the nonlinear optical crystal and the two directions of polarization intersect perpendicularly to each other, the formula EQU P.sub.SHG =1/4d.sub.eff.sup.2 (P.sub.1.sup.2 +P.sub.2.sup.2)
obtains, wherein deff represents the effective nonlinear optical constant, Pl represents the intensity of the first longitudinal mode, and P2 represents the intensity of the second longitudinal mode. Therefore, the first longitudinal mode and the second longitudinal mode are stable, and no mode coupling occurs therebetween.
Therefore, as indicated in the literature cited above, various attempts have heretofore been made to set by using a means for adjusting a difference in phase, such as a quarter-wave plate, such that directions of polarization in two longitudinal modes may intersect perpendicularly to each other and may respectively incline 45.degree. with respect to an optic axis of a nonlinear optical crystal.
However, with conventional optical wavelength converting apparatuses, even if a means for adjusting a difference in phase is utilized, drift and noise inevitably occur in wavelength-converted waves which are outputted from the optical wavelength converting apparatuses.